Question

a set of average city temperatures in december are normally distributed with a mean of 16.3° C and a standard deviation of 2°C. What proportion of temperatures are between 12.9°C and 14.9°C?

Answer 1

We have been given that a set of average city temperatures in december are normally distributed with a mean of 16.3° C and a standard deviation of 2°C. We are asked to find the proportion of temperatures that are between 12.9°C and 14.9°C.

First of all, we will find the z-score corresponding to 12.9°C and 14.9°C using z-score formula.

`z=(x-\mu)/(\sigma)`

`z=(12.9-16.3)/(2)`

`z=(-3.4)/(2)=-1.7`

Similarly, we will find z-score corresponding to 14.9°C.

`z=(14.9-16.3)/(2)`

`z=(-1.4)/(2)=-0.7`

Now we need to find probability of z-score between
`-1.7\text{ and }-0.7`.

`P(-1.7<z<-0.7)=P(z<-0.7)-P(z<-1.7)`

Using normal distribution table, we will get:

`P(-1.7<z<-0.7)=0.24196-0.04457`

`P(-1.7<z<-0.7)=0.19739`

Therefore,
`0.19739` of temperatures are between 12.9°C and 14.9°C.